Garcke, Harald ; Lam, Kei Fong 
; Sitka, Emanuel ; Styles, Vanessa
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Mathematical Models and Methods in Applied Sciences |
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| Verlag: | WORLD SCIENTIFIC PUBL CO PTE LTD |
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| Ort der Veröffentlichung: | SINGAPORE |
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| Band: | 26 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 06 |
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| Seitenbereich: | S. 1095-1148 |
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| Datum: | 2016 |
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| Institutionen: | Mathematik
Mathematik > Prof. Dr. Harald Garcke |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1142/S0218202516500263 | DOI |
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| Stichwörter / Keywords: | DIFFUSE INTERFACE MODEL; FINITE-ELEMENT APPROXIMATION; PHASE FIELD MODEL; MIXTURE MODEL; SIMULATION; SYSTEM; CANCER; FLOW; CALIBRATION; EXPRESSION; Tumour growth; diffuse interface model; Cahn-Hilliard equation; chemotaxis; Darcy's flow; matched asymptotic expansions; stability analysis; finite element computations |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 42107 |
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Zusammenfassung
Using basic thermodynamic principles we derive a Cahn-Hilliard-Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and proliferation. In contrast to earlier works, the model is based on a volume-averaged velocity and in particular includes active transport mechanisms which ensure thermodynamic consistency. We perform a formally matched ...
Zusammenfassung
Using basic thermodynamic principles we derive a Cahn-Hilliard-Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and proliferation. In contrast to earlier works, the model is based on a volume-averaged velocity and in particular includes active transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several sharp interface models. Some of them are classical and some are new which for example include a jump in the nutrient density at the interface. A linear stability analysis for a growing nucleus is performed and in particular the role of the new active transport term is analysed. Numerical computations are performed to study the influence of the active transport term for specific growth scenarios.
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